Re-using a tune for a new song is a time-honored folk theft tradition. But if I take a song and re-write it to the tune and theme of the original but change it so that it has a different message, is it a parody if it isn't humorous?

For example (apologizes to the great Tom Paxton!):

Imam, I'm a volunteer and I've just arrived in camp
I've come to wear the suicide vest and join jihad tramp
And I want to do my duty but one thing I do implore
You must give me lessons, Imam, for I've never died before.

There are rumors in the camp about the enemy
They say that when you see him he looks just like you and me.
But you deny it Imam, and this is a holy war,
I hope you will be patient for I've never died before.

This is close enough to be Tom Paxton's original song -- it can't be mistaken for anything else -- and yet I've changed it in such ways that I, for one, don't find it funny.

Is it a parody? Or what?